On any surface which fulfils the required continuity conditions, the shortest path between two points on the surface is along the are of a geodesic curve. On the surface of a sphere the geodesic curves are the great circles and the shortest path between any two points on this surface is along the arc of a great circle, but on the surface of an ellipsoid of revolution, the geodesic curves are not so easily defined except that the equator of this ellipsoid is a circle and its meridians are ellipses.
